This paper investigates an investment and reinsurance problem with delay and common shock dependence under the mean-variance utility framework. We first use Heston's SV model to depict the financial market and two-dimensional Poisson process with common shock dependence to characterize the surplus process. We then introduce the past performance and use it to derive the wealth process depicted by the stochastic delay differential equation. Applying the stochastic control theory within the framework of the game theory, and stochastic control theory with delay, we derive an extended Hamilton-Jacobi-Bellman equation with delay. By solving the equation, we obtain the equilibrium strategy and the corresponding equilibrium value function. We also provide a numerical example to analyze the effects of delay parameters and co-shocks parameters on equilibrium strategy and explain why such effects occur.

本文研究了均值-方差效用框架下具有延迟和共同冲击依赖的投资和再保险问题。我们首先使用 Heston 的 SV 模型来描述金融市场和具有共同冲击依赖性的二维泊松过程来表征剩余过程。然后我们引入过去的表现，并用它推导出随机时滞微分方程所描绘的财富过程。应用博弈论框架内的随机控制理论和带时滞的随机控制理论，推导了带时滞的扩展Hamilton-Jacobi-Bellman方程。通过求解方程，我们得到了均衡策略和对应的均衡价值函数。